Let us investigate the number of prime factors of integers.

Figure~\ref{fig:scatter_plot_of_prime_factors} shows the number of prime
factors for each integer less than 100.

\begin{center}
    \begin{figure}[!hbtp]
        \includegraphics[width=5cm]{src/scatter_plot_of_prime_factors.pdf}
        \caption{The number of prime factors of each integer}
        \label{scatter_plot_of_prime_factors}
    \end{figure}
\end{center}

Table~\ref{tab:number_of_factors_table} shows these counts for \(95\leq
n\leq 100\).

\begin{center}
    \begin{table}[!hbtp]
        \input{tex/number_of_factors_table.tex}
    \end{table}
\end{center}

The number with the most prime factors
has\input{tex/largest_number_of_factors} prime factors.

The number of factors is probably related to the number of primes which has
a lower bound given by:

\small
\[
\pi(n)=\frac{n}{\log{n}}=\input{tex/series_expansion_for_lower_bound.tex}
\]
